Results 151 to 160 of about 1,238 (176)

The set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges’ sense

Journal of Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nevena Z. Petrovic, Miroslav S. Pranic, Marija P. Stanic, Tatjana V. Tomovic Mladenovic   +3 more
openaire   +2 more sources

Gaussian quadrature rules and numerical examples for strong extensions of mass distribution functions

Journal of Computational and Applied Mathematics, 1999
The theory of strong moment problems has provided Gaussian quadrature rules for approximate integration with respect to strong distributions. In Hagler (Ph.D. Thesis, University of Colorado, Boulder, 1997) and Hagler et al.
Brian A. Hagler, Philip E. Gustafson, Hagler, Brian A., Gustafson, Philip E.   +3 more
exaly   +2 more sources

On Generating Gaussian Quadrature Rules

1979
Given a mass distribution dσ(x) on the (finite or infinite) interval (a,b), where σ(x) has at least n+1 points of increase, and assuming the existence of the first 2n moments of dσ(x), $${\mu _k} = \int_a^b {{x^k}} d\sigma (x),\;\;\;\;k = 0,1,2,...,2n - 1$$ (1.1) it is well known that the n-point Gaussian quadrature rule associated with the ...
openaire   +1 more source

Some error expansions for certain Gaussian quadrature rules

Journal of Computational and Applied Mathematics, 2003
Complex-variable methods are used to obtain some error expansions for certain quadrature rules over the interval [−1,1]
Smith, H.V.
exaly   +2 more sources

Gaussian quadrature rules using function derivatives

IMA Journal of Numerical Analysis, 2009
For finite positive Borel measures supported on the real line we consider a new type of quadrature rule with maximal algebraic degree of exactness that involves function derivatives. We prove the existence of such quadrature rules and describe their basic properties.
G. V. Milovanovic, A. S. Cvetkovic
openaire   +1 more source

Anti-Gaussian quadrature rules related to orthogonality on the semicircle

Numerical Algorithms
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aleksandra S. Milosavljevic, Marija P. Stanic, Tatjana V. Tomovic Mladenovic   +2 more
openaire   +1 more source

Error bounds for Gaussian quadrature rules using linear kernels

International Journal of Computer Mathematics, 2015
It is well-known that the remaining term of a n-point Gaussian quadrature depends on the -order derivative of the integrand function. Discounting the fact that calculating a -order derivative requires a lot of differentiation, the main problem is that an error bound for a n-point Gaussian quadrature is only relevant for a function that is ...
Mohammad Masjed-Jamei, Iván Area
openaire   +1 more source

Gaussian Quadrature Rule using ε-Quasiorthogonality

2018
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using ε-quasiorthogonality, for the approximation of integrals of the form \int f(x)d α(x). The measure α(\cdot) can be arbitrary as long as it possesses finite moments μn for sufficiently large n.
Létourneau, Pierre-David, Darve, Eric
openaire   +1 more source

On The Construction of Some Gaussian Quadrature Rules

1979
In this paper we give a survey of asymptotic formulas for the zeros of ultraspherical polynomials. The approximations that they yield can be employed for selecting initial guesses in a 5th order iterative method used by Lether in the particular case of the zeros of Legendre polynomials.
openaire   +1 more source

Slepian functions on the sphere, generalized Gaussian quadrature rule

Inverse Problems, 2004
Summary: Denote by \({\mathbf K}\) the operator of `time-band-time' limiting on the surface of the sphere, and consider the problem of computing singular vectors of \({\mathbf K}\). This problem can be reduced to a simpler task of computing eigenfunctions of a differential operator, if a differential operator which commutes with \({\mathbf K}\) and has
openaire   +2 more sources